Maximal determinant over a certain class of matrices and its application to D-optimality of designs |
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Authors: | K. Filipiak A. Markiewicz R. Różański |
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Affiliation: | 1. Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, Poland;2. Technical Institute, The State Vocational School of Higher Education, Teatralna 25, 66-400 Gorzów Wlkp., Poland |
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Abstract: | It is known that some optimality criteria of experimental designs are functionals of the eigenvalues of their information matrices. In this context we study the problem of maximizing the determinant of , , over the class of t-by-t permutation matrices, and the determinant of , , over the class of t-by-t permutation matrices with zero diagonal (derangement matrices). The results are used to characterize D-optimal complete block designs under an interference model. |
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